University of Guilan Journal of Algebra and Related Topics 2345-3931 9 1 2021 06 01 Some classes of perfect annihilator-ideal graphs associated with commutative rings 21 29 4805 10.22124/jart.2021.17227.1214 EN M. Adlifard Department of Mathematics, Roudbar Branch Islamic Azad University, Roudbar, Iran Sh. Payrovi Department of Mathematics, Imam Khomeini International University, Qazvin, Iran Journal Article 2020 07 27 Let $R$ be a commutative ring and let $\Bbb A(R)$ be<br />the set of all ideals of $R$ with nonzero annihilator.<br />The annihilator-ideal graph of $R$ is defined as the graph<br />${A_I}(R)$ with the vertex set $\Bbb A(R)^*=\Bbb A(R)\setminus\{0\}$ and two<br />distinct vertices $I$ and $J$ are adjacent if and only if<br />${\rm Ann}_R(IJ)\neq{\rm Ann}_R(I) \cup{\rm Ann}_R(J)$. In this paper, perfectness of<br />${A_I}(R)$ for some classes of rings is investigated. https://jart.guilan.ac.ir/article_4805_94dd66e60e677c95c058bec639a9936b.pdf